[jackchilvers]

Dear all,

I am having an issue getting my head around the tensor/Einstein notation with regards to the multiplication of three tensors within a transport equation. For the purposes of code implementation, I would like to expand out the notation to make terms explicitly clear. For example, if you have two tensors multiplied like so:

A_{ij}B_{ik}A_{jk}

where A and B are 3x3 matrices, how would one go about expanding these terms? Your help is much appreciated (even a reference text on the subject at hand).

Jack

[truffaldino]

a[1,2]*b[1,3]*a[2,3]+a[2,1]*b[2,2]*a[1,2]+a[1,1]*b[1,3]*a[1,3]+
a[3,3]*b[3,2]*a[3,2]+a[3,3]^2*b[3,3]+a[3,2]*b[3,2]*a[2,2]+
a[1,2]*b[1,2]*a[2,2]+a[1,3]*b[1,1]*a[3,1]+a[3,2]*b[3,1]*a[2,1]+
a[2,3]*b[2,1]*a[3,1]+a[2,1]*b[2,1]*a[1,1]+a[1,3]*b[1,2]*a[3,2]+
a[1,1]^2*b[1,1]+a[1,1]*b[1,2]*a[1,2]+a[2,2]*b[2,1]*a[2,1]+
a[1,2]*b[1,1]*a[2,1]+a[2,2]*b[2,3]*a[2,3]+a[2,1]*b[2,3]*a[1,3]+
a[3,2]*b[3,3]*a[2,3]+a[3,1]*b[3,1]*a[1,1]+a[3,3]*b[3,1]*a[3,1]+
a[2,2]^2*b[2,2]+a[2,3]*b[2,2]*a[3,2]+a[3,1]*b[3,3]*a[1,3]+
a[2,3]*b[2,3]*a[3,3]+a[3,1]*b[3,2]*a[1,2]+a[1,3]*b[1,3]*a[3,3]

[jackchilvers]

Very comprehensive, thank you very much truffaldino!